Posted by **isa** on Tuesday, February 17, 2009 at 9:41pm.

suppose an arithmetic sequence and a geometric sequence with common ration r have the same first two terms. show that the third term of the geometric series is r^2/(2r-1) tomes the third term of the arithmetic sequence

- math -
**Reiny**, Tuesday, February 17, 2009 at 10:10pm
the first 3 terms of the AS are a, a+d, a+2d

the first 3 terms of the GS are a, ar, ar^2

you said the second terms are equal

then a+d = ar

d = ar-a

so third term of GS/third term of AS

= ar^2/(a+2d)

= ar^2(a + 2(ar-a)

= ar^2/(a + 2ar - 2a)

= ar^2/(2ar - a) now divide top and bottom by a

= r^2/(2r-1)

- math -
**Anonymous**, Sunday, March 1, 2015 at 9:36am
swaggot swag

## Answer this Question

## Related Questions

- Maths - 1..The first 2 terms of a geometric progression are the same as the ...
- Math - A sequence is formed by adding together the corresponding terms of a ...
- math - Determine whether each sequence is arithmetic or geometric. Find the next...
- Math Help!!! - determine whether each sequence is arithmetic or geometric. find ...
- Maths - An arithmetic and a geometric sequence have the same first terms.(2).......
- math - in an arithmetic sequence the common difference is equal to 2.the first ...
- MATH - A new sequence is formed by adding together the corresponding terms of a ...
- math... - how can I tell if a sequences is airthmetic, geometric or neither? ...
- math - The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of ...
- Maths - Eric thinks of 2 sequences.One is geometric and the other arithmetic....